Factorization of differential operators with rational functions coefficients

Journal of Symbolic Computation

Volumn 24, Issue 5, 1997, Pages 537-561

  Van Hoeij, Mark ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031281466     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsco.1997.0151     Document Type: Article

References (24)

1. Abramov, A., Bronstein, M., Petkovšek, M. (1995). On polynomial solutions of linear operator equations. Proceedings ISSAC'95, ACM Press, pp. 290-296.
2. Beckermann, B., Labahn, G. (1992). A uniform approach for Hermite Padé and simultaneous Padé Approximants and their matrix-type generalizations, Numerical Algorithms 3, 45-54.
3. Beckermann, B., Labahn, G. (1994). A uniform approach for the fast computation of matrix-type Padé approximants, SIAM J. Matrix Anal. Appl. 804-823.
4. Beke, E. (1894). Die Irreduzibilität der homogenen linearen Differentialgleichungen, Math. Ann. 45, 278-294.
5. Bertrand, D., Beukers, F. (1985). Équations différentielles linéaires et majorations de multiplicités, Ann. Sci. École Norm. Sup. (4) 18, 181-192.
6. Bronstein, M. (1992). Linear ordinary differential equations: breaking through the order two barrier. Proceedings ISSAC'92, ACM Press, 42-48.
7. Bronstein, M. (1994). An improved algorithm for factoring linear ordinary differential operators. Proceedings ISSAC'94, Oxford, U.K., ACM Press, 336-340.
8. Derksen, H. (1994). An algorithm to compute generalized Padé-Hermite forms Manuscript. Available by ftp at daisy.math.unibas.ch in /pub/hderksen/pade.dvi.
9. Grigor'ev, D.Y. (1990). Complexity of factoring and calculating the GCD of linear ordinary differential operators. J. Symbolic Comput. 10, 7-37.
10. Hendriks, P.A., van der Put, M. (1995). Galois action on solutions of a differential equation, J. Symbolic Comput.
11. van Hoeij, M. (1996). Rational Solutions of the Mixed Differential Equation and its Application to Factorization of Differential Operators, Proceedings ISSAC'96, pp. 219-225.
12. van Hoeij, M. (1997). Formal solutions and factorization of differential operators with power series coefficients, J. Symbolic Comput. To appear.
13. van Hoeij, M., Weil, J.A. (1997). An algorithm for computing invariants of differential Galois groups, J. Pure Appl. Algebra. To appear.
14. Kovacic, J. (1986). An algorithm for solving second order linear homogeneous differential equations, J. Symbolic Comput. 2 3-43.
15. Loewy, A. (1906). Über vollständig reduzible lineare homogene Differentialgleichungen, Math. Ann. 62, 89-117.
16. Ore, O. (1932). Formale Theorie der linearen Differentialgleichungen (Zweiter Teil), J. Reine Angew. Math. 168, 233-252.
17. Ore, O. (1933). Theory of non-commutative polynomial rings, Ann. of Math. 34, 480-508.
18. Schwarz, F. (1989). A factorization algorithm for linear ordinary differential equations. Proceedings of ISSAC'89, ACM Press, pp. 17-25.
19. Singer, M.F. (1981). Liouvillian solutions of n-th order homogeneous linear differential equations. Amer. J. Mat. 103, 661-682.
20. Singer, M.F. (1996). Testing reducibility of linear differential operators: a group theoretic perspective, Appl. Alg. Eng. Comm. Comp. 7, 77-104.
21. Sommeling, R. (1993). Characteristic classes for irregular singularities, Ph.D. thesis, University of Nijmegen.
22. Tsarev, S.P. (1994). On the problem of factorization of linear ordinary differential operators, Prog. Comput. Software, v. 20, 1, 27-29.
23. Tsarev, S.P. (1996). An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator, Proceedings ISSAC'96.
24. Weil, J.A. (1995). Constantes et polynômes de Darboux en algèbre différentielle : application aux systèmes différentiels linéaires, PhD dissertation, École Polytechnique.